Micro-Electro-Mechanical Systems (or MEMS) devices are becoming increasingly prevalent as low-cost, compact devices having a wide range of applications. Uses include pressure sensors, accelerometers, gyroscopes, microphones, digital mirror displays, microfluidic devices, biosensors, chemical sensors, and others.
MEMS transducers include both actuators and sensors. In other words they typically convert an electrical signal into a motion, or they convert a motion into an electrical signal. They are typically made using standard thin film and semiconductor processing methods. As new designs, methods and materials are developed, the range of usages and capabilities of MEMS devices can be extended.
MEMS transducers are typically characterized as being anchored to a substrate and extending over a cavity in the substrate. Three general types of such transducers include a) a cantilevered beam having a first end anchored and a second end cantilevered over the cavity; b) a doubly anchored beam having both ends anchored to the substrate on opposite sides of the cavity; and c) a clamped sheet that is anchored around the periphery of the cavity. Type c) is more commonly called a clamped membrane, but the word membrane will be used in a different sense herein, so the term clamped sheet is used to avoid confusion.
Sensors and actuators can be used to sense or provide a displacement or a vibration. For example, the amount of deflection δ of the end of a cantilever in response to a stress cy is given by Stoney's formulaδ=3σ(1−v)L2/ET2  (1),where v is Poisson's ratio, E is Young's modulus, L is the beam length, and t is the thickness of the cantilevered beam. In order to increase the amount of deflection for a cantilevered beam, one can use a longer beam length, a smaller thickness, a higher stress, a lower Poisson's ratio, or a lower Young's modulus. The resonant frequency of vibration of an undamped cantilevered beam is given byf=ω0/2π=(k/m)1/2/2π,  (2),where k is the spring constant and m is the mass. For a cantilevered beam of constant width w, the spring constant k is given byk=Ewt3/4L3  (3).It can be shown that the dynamic mass m of an oscillating cantilevered beam is approximately one quarter of the actual mass of pwtL (ρ being the density of the beam material), so that within a few percent, the resonant frequency of vibration of an undamped cantilevered beam is approximatelyf˜(t/2πL2) (E/ρ)1/2  (4).For a lower resonant frequency one can use a smaller Young's modulus, a smaller thickness, a longer length, or a larger density. A doubly anchored beam typically has a lower amount of deflection and a higher resonant frequency than a cantilevered beam having comparable geometry and materials. A clamped sheet typically has an even lower amount of deflection and an even higher resonant frequency.
Based on material properties and geometries commonly used for MEMS transducers the amount of deflection can be limited, as can the frequency range, so that some types of desired usages are either not available or do not operate with a preferred degree of energy efficiency, spatial compactness, or reliability. For example, using typical thin film transducer materials for an undamped cantilevered beam of constant width, Equation 4 indicates that a resonant frequency of several megahertz is obtained for a beam having a thickness of 1 to 2 microns and a length of around 20 microns. However, to obtain a resonant frequency of 1 kHz for a beam thickness of about 1 micron, a length of around 750 microns would be required. Not only is this undesirably large, a beam of this length and thickness can be somewhat fragile. In addition, typical MEMS transducers operate independently. For some applications independent operation of MEMS transducers is not able to provide the range of performance desired.
Energy harvesting devices convert ambient energy from the environment into electrical energy. An example is a piezoelectric energy harvesting device that converts mechanical strain into electric current or voltage. Typically, these devices operate most efficiently when oscillating at mechanical resonance. However, many of the prevalent frequencies of motion in the environment tend to be in the low kilohertz range (including pressure waves and mechanical vibrations) down to 100 Hz and below (such as vibration from a motor powered at 60 Hz). As discussed above, a piezoelectric cantilevered beam having a resonant frequency in this range can be undesirably large and fragile.
Accordingly, there is a need for a MEMS transducer design and method of operation that provides low cost, compact, or reliable energy harvesting devices capable of efficiently converting externally produced excitations to electrical energy especially when the excitations are in a frequency range that is below a few kilohertz.